Digital filter for IQ-generation, noise shaping and neighbour channel suppression

ABSTRACT

A polyphase filter of order x.N that is building N allpass filters of order x.N according to the present invention has a structure of an allpass filter of order x comprising delay elements with a delay 1 and at least one multiplier, wherein all delay elements with a delay of 1 are replaced by delay elements with a delay of N and the sampling rate of f s ′=f s /N with f s  being the sampling rate of the input signal.  
     Preferably the multiplier included in the structure of the allpass filter of order x comprises N-time multiplex multiplication coefficients that are used in a predetermined order.

DESCRIPTION

[0001] The present invention relates to the digital generation of acomplex baseband signal and in particular to an efficient realization ofa polyphase-filter which can be used therefore and also for otherpurposes.

[0002] The German Patent Application DE 43 32 735 A1 “Verfahren zurdigitalen Erzeugung eines komplexen Basisbandsignals” describes analgorithm for the generation of a complex baseband signal which makesuse of a polyphase-filter. This Patent Application also describes thatthe branch filters of the polyphase-filter should be realized as allpassfilters.

[0003] The paper “Entwurf und Realisierung diskreter Filterbänke”,published by Shaker, ISBN 3-8265-0366-X, from Torsten Leickel explainshow to design such polyphase-filters with allpass branch filters.

[0004] In this case, the input signal of the polyphase-filter ismultiplexed into N different allpass filters. Therefore, N allpassfilters have to be realized with N being the decimation factor of thepolyphase filter. This design leads to high realization costs for thepolyphase-filter. Also, only a restricted amount of IF-frequencies canbe realized with this structure, since the IF-frequencies can only bechosen to F_(IF)=m·F+L·F/N with F being the sampling rate of the filterinput signal, L being a natural constant between$\frac{{- N} - 1}{2}\ldots \frac{N - 1}{2}$

[0005] and m being a natural constant.

[0006] Further, EP 0 597 255 A1 “Empfänger für ein digitalesRundfunksignal mit digitaler Signalverarbeitung” discloses an efficientrealization of an algorithm for the generation of a complex basebandsignal. To optimize the realization of the digital signal processing aswitchable allpass filter is used. However, this realization has thedisadvantage that no digital neighbour channel suppression/noise shapingcan be realized and the IF-frequency can only be chosen toF_(IF)=m·F±F/4 with F being the IQ-filter input sampling rate and mbeing a natural constant.

[0007] However, all of the above IQ-generators are quite restricted inrespect to the used Intermediate Frequency (IF) and therewith in respectto possible sampling frequencies of the A/D converter converting the IFsignal into a signal suitable for a following digital basebandprocessing since the output frequency of the generation is fixedaccording to certain standards and the input frequency of the IQgeneration (i. e. the IF frequency) strongly depends on the usedIQ-filter and the needed output frequency.

[0008] Therefore, it is an object underlying the present invention toprovide a polyphase-filter which can be used for the IQ-generation andan IQ-generator providing an increased number of possible IntermediateFrequencies, i. e. more flexibility in the choosing of the samplingfrequency of the A/D converter preceding the IQ generation.

[0009] A polyphase filter consisting of N branch allpass filters oforder x.N to filter an input signal t(k) according to the presentinvention is defined in independent claim 1. Preferred embodimentsthereof are defined in dependent claims 2 to 7.

[0010] The polyphase filter according to the present invention has lowrealization costs, since only a very small amount of adders andmultipliers are required. In a preferred embodiment every neededmultiplier is realized by at least one shift register, at least oneadder and at least on subtracter, so that the realization costs areadditionally decreased.

[0011] Furthermore, the using of a multiplexing technology allows a veryeasy adaptation to a different “number” of branch filters and therewithto a different IF frequency.

[0012] An IQ-generator according to the present invention is defined inindependent claim 8. Preferred embodiments thereof are defined independent claims 9 and 10.

[0013] The IQ generator according to the present invention allows a veryeasy doubling of possible Intermediate Frequencies for a given polyphasefilter consisting of N branch allpass filters of order x.N used therein,since signal symmetrics are used in an efficient way.

[0014] Preferably, the IQ-generator according to the present inventioncomprises a polyphase filter according to the present invention whichallows to replace the expensive analog filters in front of theA/D-converter by weak, cheap filters, since the polyphase filteraccording to the present invention allows a noise shaping and neighbourchannel suppression in an easy way so that the effective resolution ofthe A/D-converter will be increased.

[0015] The present invention which uses and modifies the structure ofconventional allpass filters first order to realize a polyphase filterof order x.N will be better understood from the following detaileddescription of exemplary embodiments thereof taken in conjunction withthe accompanying drawings, wherein

[0016]FIG. 1 shows a block diagram of the N time multiplexed branchallpass filters of the polyphase filter according to a first preferredembodiment of the present invention;

[0017]FIGS. 2a and 2 b show how the design of the polyphase branchallpass filters of order N according to the first preferred embodimentof the present invention was achieved,

[0018]FIG. 3 shows polyphase branch allpass filters according to asecond preferred embodiment of the present invention;

[0019]FIG. 4 shows how the design of the polyphase filter according tothe second preferred embodiment of the present invention was achieved;

[0020]FIG. 5 shows a block diagram of the system environment of anIQ-filter;

[0021]FIG. 6 shows a block diagram of a digital IQ-filter;

[0022]FIG. 7 shows a block diagram of a digital IQ-filter in case ofquarter period sampling;

[0023]FIG. 8 shows a block diagram of the digital IQ-filter according toa preferred embodiment of the present invention; and

[0024]FIG. 9 shows an efficient realization of the IQ-filter shown inFIG. 8.

[0025] In the following the first preferred embodiment of a polyphasefilter according to the present invention will be explained inconnection with FIGS. 1 and 2.

[0026]FIG. 2a shows a state of the art allpass filter of order 1 whichcomprises two delay elements 101 and 102, one adder 103, one subtracter104 and one multiplier 105. Both delay elements have a delay T and themultiplier has a multiplication factor α. The structure of the state ofthe art allpass filter of order 1 shown in FIG. 2a is such that an inputsignal t(k) is fed to an input delay element 101 and as minuent to thesubtracter 104. The delayed input signal output by the delay element 101is input as a first summand to the adder 103 that produces and outputsthe output signal u(k) of the allpass filter. The output signal u(k) isfed to an output delay element 102 which outputs the subtrahend for thesubtracter 104. The difference calculated by the subtracter 104 getsmultiplied with the multiplication factor a by the multiplier 105 andthe resulting product is supplied as second summand to the adder 103which adds its first and second summands to produce its output signal.

[0027] Equation (1) describes the transfer function of a polyphaselowpass filter with N filter branches, e. g. shown in “Multirate digitalsignal processing: multirate systems, filterbanks, wavelets”, by N. J.Fliege, ISBN 0-471-93976-5: $\begin{matrix}{{H_{lp}(z)} = {\sum\limits_{r = 0}^{N - 1}{z^{- r}{H_{r}\left( z^{N} \right)}}}} & (1)\end{matrix}$

[0028] with z=e^(jΩ) $\begin{matrix}{\Omega = {2\pi \frac{f}{f_{s}}}} \\{j = \sqrt{- 1}}\end{matrix}$

[0029] As described in the DE 43 32 735 A1 or the publication “A newdesign method for polyphase filters using allpass sections” by W. Drews& L. Garrsi, IEEE Transactions on Circuits and Systems, Vol. CAS33, No.3, March 1986, the branch filters can be chosen as state of the artallpass filters. The transfer function of such an allpass filter oforder 1 which is shown in FIG. 2a is given in equation (2).$\begin{matrix}{{H_{{ap},{1^{st}\quad {order}}}\quad (z)} = {\frac{U(z)}{T(z)} = {\frac{\alpha + z^{- 1}}{1 + {\alpha \quad z^{- 1}}} = \frac{{\alpha \quad z} + 1}{z + \alpha}}}} & (2)\end{matrix}$

[0030] With equations (1) and (2) follows the transfer function of abranch allpass filter of the polyphase filter with one coefficient asshown in equation (3): $\begin{matrix}{{H_{r}\left( z^{N} \right)} = \frac{{\beta_{r}z^{N}} + 1}{z^{N} + \beta_{r}}} & (3)\end{matrix}$

[0031] Therefore, with equations (1) and (3) follows the transferfunction of the polyphase lowpass filter as shown in equation (4):$\begin{matrix}{{H_{lp}(z)} = {\sum\limits_{r = 0}^{N - 1}{z^{- r}\frac{{\beta_{r}z^{N}} + 1}{z^{N} + \beta_{r}}}}} & (4)\end{matrix}$

[0032] To realize a polyphase lowpass filter with a transfer function asshown in equation (4) according to the present invention, the N branchallpass filters are realized time-multiplexed with a sampling rate off_(s)′=f_(s)/N with f_(s) being the sampling rate of the polyphasefilter input signal t(k).

[0033]FIG. 2b shows the structure of these N time-multiplexed allpassfilters of order N with a sampling rate of f_(s)′=f_(s)/N which is onlydifferent to the allpass filter first order shown in FIG. 2a in that thedelay elements now have order N and the sampling rate is decreased,since the sampling rate decimation by N at the output of the polyphasefilter is shifted to the input of the branch filter.

[0034] The transfer function of each of the N time-multiplexed allpassfilters is calculated as follows: $\begin{matrix}\begin{matrix}{{{With}\quad f_{s}^{\prime}} = {{\frac{f_{s}}{N}\quad {and}\quad \Omega^{\prime}} = {2\pi \quad \frac{f}{f_{s}^{\prime}}\quad {follows}\quad {equation}\quad \text{(5):}}}} \\{\Omega^{\prime} = {{2\pi \quad \frac{Nf}{f_{s}}} = {N\quad {\Omega.}}}}\end{matrix} & (5)\end{matrix}$

[0035] With z′=e^(jΩ) and equation (5) follows equation (6):

z′=e^(jΩ′)=e^(jNΩ)=z^(N)  (6)

[0036] With equation (6) follows for the transfer function (7) of the Ntime-multiplexed allpass filters N^(th) order in consideration of thedelay caused by the time-multiplex: $\begin{matrix}{{H_{{ap}^{\prime},{1^{st}\quad {order}}}\quad \left( z^{N} \right)} = {\frac{U\left( z^{N} \right)}{T\left( z^{N} \right)} = {z^{- r}\frac{{\alpha z}^{N} + 1}{z^{N} + \alpha}}}} & (7)\end{matrix}$

[0037] with r=0, 1, . . . N−1.

[0038] In the preferred embodiment, additionally the coefficient α ofthe N time-multiplex allpass filters is replaced by N time-multiplexedcoefficients α₀, . . . α_(N−1) as shown in equation (8):

α(k)=α_((k mod N))  (8)

[0039] The N time-multiplexed allpass filters of order N with thesampling rate f_(s)′=f_(s)·N included in the polyphase filter accordingto the first preferred embodiment of the present invention have now thefollowing transfer functions as shown in equation (9): $\begin{matrix}{{H_{{ap}_{r}^{\prime},\quad {1^{st}\quad {order}}}\quad \left( z^{N} \right)} = {\frac{U\left( z^{N} \right)}{T\left( z^{N} \right)} = {z^{- r}\frac{{\alpha_{r}z^{N}} + 1}{z^{N} + \alpha_{r}}}}} & (9)\end{matrix}$

[0040] with r=0, 1, . . . N−1.

[0041] The block diagram of this polyphase branch filter realizationaccording to the first preferred embodiment of the present invention isshown in FIG. 1 which basically shows the same structure as FIG. 2b, butthe multiplier now comprises N time-multiplexed coefficients asdescribed above.

[0042] Therefore, the polyphase filter according to the first preferredembodiment of the present invention comprises: a first delay element 1with a delay N that receives the input signal t(k); a first adder 3 thatreceives the output signal of said first delay element 1 at a firstinput for the first summand; a second delay element 2 with a delay Nthat receives the sum produced by said first adder 3; a first subtracter4 that receives the input signal t(k) at a first input for the minuendand the output signal of the second delay element 2 at a second inputfor the subtrahend; and a first multiplier 5 that receives thecalculated difference of the first subtracter 4, multiplies itrespectively with a predetermined multiplication coefficient α(k) andoutputs the calculated product to a second input of the first adder 3that receives the second summand, wherein in the sum produced by saidfirst adder 3 builds the output signal u(k) of the filter.

[0043] The allpass branch filters of the polyphase filters can of coursebe of higher order than of order 1. The following second preferredembodiment according to the present invention described in connectionwith FIGS. 3 and 4 shows how to create a polyphase lowpass filter withbranch filters second order from a state of the art allpass filtersecond order.

[0044] Such state of the art allpass filter second order is shown inFIG. 4. The difference to the state of the art allpass filter firstorder shown in FIG. 2a is that the output signal u(k) is not the sumgenerated by first adder 103, but a second filter stage follows togenerate this signal. Therefore, the output signal u(k) is generated asa sum signal of a further adder 106 that receives the output signal ofthe output delay element 102 as a first summand. The second summand ofsaid further adder 106 is generated by multiplying the difference of thesum signal produced by the adder 103 and the delayed output signal u(k)by a multiplication factor χ with a further multiplier 109. The timedelayed output signal u(k) is generated by a second output delay element107.

[0045] The transfer function of such an allpass filter second order isshown in equation (11): $\begin{matrix}{{H_{{{ap}.\quad 2^{nd}}\quad {order}}\quad (z)} = {\frac{U(z)}{T(z)} = {\frac{{\alpha z} + 1}{z + \alpha} \cdot \frac{{\chi z} + 1}{z + \chi}}}} & (11)\end{matrix}$

[0046] Therefore, with the transfer function of a polyphase lowpassfilter described in equation (1), the transfer function for thepolyphase allpass branch filters with 2 coefficients follows as shown inequation (12): $\begin{matrix}{{H_{r}\left( Z^{N} \right)} = {\frac{{\beta_{r}z^{N}} + 1}{z^{N} + \beta_{r}} \cdot \frac{{\delta_{r}z^{N}} + 1}{z^{N} + \delta_{r}}}} & (12)\end{matrix}$

[0047] With equations (1) and (12) follows for the transfer function ofthe polyphase lowpass filter the following equation (13):$\begin{matrix}{{H_{1p}\left( z^{N} \right)} = {\sum\limits_{r = 0}^{N - 1}{z^{- r}{\frac{{\beta_{r}z^{N}} + 1}{z^{N} + \beta_{r}} \cdot \frac{{\delta_{r}z^{N}} + 1}{z^{N} + \delta_{r}}}}}} & (13)\end{matrix}$

[0048] For the polyphase lowpass filter with branch allpass filters oforder 2.N according to the present invention follows that all delayelements of order 1 shown in FIG. 4 have to be replaced with delayelements of order N and the sampling rate of each branch input signal ischanged to f′_(s)=f_(s)/N with f_(s) being the sampling rate of theinput signal t(k).

[0049] According to the second preferred embodiment of the presentinvention the polyphase filter with branch filters of order 2.Nadditionally respectively comprises N time-multiplex coefficients α_(r)and χ_(r) with r=0, 1, . . . N−1 instead of the coefficients α and χshown in FIG. 4. Therefore, the polyphase filter according to the secondembodiment of the present invention as shown in FIG. 3 comprisesadditionally to all components shown in FIG. 1: a second adder 6 thatreceives the output signal of the second delay element 2 at a firstinput for the first summand; a third delay element 7 with a delay N thatreceives the sum produced by said second adder 6; a second subtracter 8that receives the sum produced by said first adder 3 at a first inputfor the minuend and the output signal of the third delay element 7 at asecond input for the subtrahend; and a second multiplier 9 that receivesthe calculated difference of the second subtracter 8, multiplies itrespectively with a predetermined multiplication coefficient χ(k) andoutputs the calculated product to a second input of the second adder 6that receives the second summand, wherein the sum produced by saidsecond adder 6 builds the output signal u(k) of the branch filters.

[0050] The transfer function of the N time-multiplexed allpass filters2N^(th) order included in the polyphase filter according to the secondpreferred embodiment are given in the following equation (15):$\begin{matrix}{{H_{{{ap}_{r}^{\prime}.\quad 2^{nd}}\quad {order}}(z)} = {z^{- r}{\frac{{\alpha_{r}z^{N}} + 1}{z^{N} + \alpha_{r}} \cdot \frac{{\chi_{r}z^{N}} + 1}{z^{N} + \chi_{r}}}}} & (15)\end{matrix}$

[0051] with r=0, 1, . . . N−1.

[0052] The coefficients of the N time-multiplexed allpass filters2N^(th) order can be achieved by comparing equations (13) and (15). Thecoefficients α_(r) and χ_(r) of the N time-multiplexed allpass filtersare the same as the coefficients β_(r) and δ_(r) of the polyphaselowpass filter, as it is shown in equation (16):

α_(r)=β_(r) for r=0, 1, . . . , N−1

χ_(r)=δ_(r) for r=0, 1, . . . , N−1  (16)

[0053] It can be seen from both preferred embodiments according to thepresent invention described above that the present invention allows avery easy design of polyphase filters of order x.N consisting of Nallpass filters of order x.N and having a desireable factor N. Accordingto the present invention within the structure of an allpass filter oforder x all delay elements with a delay 1 are replaced by delay elementswith a delay N and so the input sampling rate of the branch filters isdecreased to a sampling rate f_(s)′=f_(s)/N with f_(s) being thesampling rate of the input signal t(k) of the polyphase filter.

[0054] Preferably every multiplier included within the allpass filter oforder x comprises N time-multiplexed multiplication coefficients thatare used in a predetermined order, e. g. a(k)=a_((k mod N)).

[0055] Further preferably everyone of said multipliers has quantizedcoefficients so that it can be realized by at least one shift register,at least one adder and at least one subtracter.

[0056] An IQ-generator according to the present invention is describedin connection with FIGS. 5 to 9.

[0057]FIG. 5 shows on the left hand side an analog bandpass signal s(t)with a center frequency f₀ which is sampled by an A/D-converter with asampling rate f_(s). The sampled bandpass signal s(k) is passed to adigital IQ-filter according to the present invention that mixes thesampled bandpass signal s(k) to a complex baseband signal, performs asampling rate decimation with a decimation factor of N and a noiseshaping which depends on the number of branch filters N of the polyphasefilter. The output signal of the IQ-filter is the complex basebandsignal w(1)=w_(I)(1)+jw_(Q)(1) with a sampling rate of f_(s)′=f_(s)/N.

[0058]FIG. 6 shows the block diagram of the digital IQ-filter accordingto the present invention that includes a filter block 22 consisting of Ntime-multiplexed allpass filters according to the present invention. Theincoming sampled bandpass signal s(k) gets multiplied with a signal A(k)by an multiplier 21 before the resulting signal t(k) is input to the Ntime multiplexed allpass filters 22 according to the present inventionwhich outputs an output signal u(k). To generate the inphase componentw_(I)(1) of the complex baseband signal w(1) the output signal u(k) ofthe polyphase filter according to the present invention is subjected toa multiplication with the function B(k)·cos(2πf₀/f_(S)·k) in amultiplier 23 before it is supplied as a first summand to an adder 24which receives its own output signal delayed by a delay element 26 witha delay T via a switch S_(I)(k) 25 as second summand. The output signalof the adder 24 gets decimated by N in a sampling rate decimation unit27 which outputs the in-phase component w_(I)(1) of the complex basebandsignal w(1). To generate the quadrature-component w_(Q)(1) of thecomplex baseband signal w(1) the output signal u(k) of the polyphasefilter according to the present invention is subjected to amultiplication with the funktion B(k)·sin (2 πf₀/f_(S)·k) in amultiplier 28 before it is supplied as a first summand to an adder 29which receives its own output signal delayed by a delay element 31 witha delay T via a switch S_(Q)(k) 30 as second summand. The output signalof the adder 29 gets decimated by N in a sampling rate decimation unit32 which outputs the quadrature component w_(Q)(1) of the complexbaseband signal w(1).

[0059] The switch s_(I)(k) 25 for the inphase component of the complexbaseband signal and the switch S_(Q)(k) 30 for the quadrature componentof the complex baseband signal are switched in the following way:

[0060] $\begin{matrix}{{S_{1}(k)} = {{S_{Q}(k)} = \left\{ \begin{matrix}0 & \quad & {{k\quad {mod}\quad N} = 0} \\\quad & {for} & \quad \\1 & \quad & {else}\end{matrix} \right.}} & (17)\end{matrix}$

[0061] The center frequency f₀ of the A/D-converter input signal s(t) isgiven by equation (18) or (19): $\begin{matrix}{f_{0} = {f_{s}\left( {\frac{n \pm 0.5}{N} + m} \right)}} & (18) \\{f_{o} = {f_{s}\left( {\frac{n}{N} + m} \right)}} & (19)\end{matrix}$

[0062] with N: decimation factor

[0063] n: integer in the range of$\left\lbrack {{- \frac{N}{2}},\ldots \quad,\frac{N}{2}} \right\rbrack$

[0064] m: integer

[0065] A(k) and B(k) must be chosen dependent on the center frequency ofthe A/D-converter input signal. In case of a center frequency f₀calculated with equation (18) A(k) and B(k) are given by equation (20):$\begin{matrix}{{A(k)} = {{B(k)} = \left( {- 1} \right)^{{floor}\quad {(\frac{k}{N})}}}} & (20)\end{matrix}$

[0066] In case of a center frequency f₀ calculated with equation (19)A(k) is given by equation (21):

A(k)=B(k)=1  (21)

[0067] In the special case of the following equation (22):$\begin{matrix}{f_{0} = {f_{s}\left( {\frac{1}{4} + m} \right)}} & (22)\end{matrix}$

[0068] with m: integer, which is also called quarter period sampling,the carrier multiplication at the output of the modified allpass filteris not necessary. In this case, the block diagram shown in FIG. 6 can bereduced to the block diagram shown in FIG. 7.

[0069] Here, the output signal u(k) of the N time multiplexed allpassfilters 22 according to the present invention is fed directly as a firstsummand to an adder 33 which outputs the IQ-multiplexed complex basebandsignal w(1)=w_(I)(1)+jw_(Q)(1). The adder 33 receives the IQ-multiplexedcomplex baseband signal delayed by two delay elements 35, 36 each havinga delay T via a switch S7 34 as second summand. The switch 34 isswitched in the following way: $\begin{matrix}{S_{\tau} = \left\{ \begin{matrix}0 & \quad & {{{k\quad {mod}\quad N} = 0},1} \\\quad & {for} & \quad \\1 & \quad & {else}\end{matrix} \right.} & (23)\end{matrix}$

[0070] The output signal of the adder 33 gets decimated by N/2 in asampling rate decimation unit 37 which outputs the multiplexed complexbaseband signal w(1).

[0071] Depending on the required sideband for the IQ-generation, thefactor A(k) is calculated by equation (24) or equation (25):$\begin{matrix}{{A(k)} = \left( {- 1} \right)^{{floor}{(\frac{k}{2})}}} & (24) \\{{A(k)} = \left( {- 1} \right)^{{floor}{(\frac{k - 1}{2})}}} & (25)\end{matrix}$

[0072] As mentioned above, the output signal of the IQ-filter describedin FIG. 7 is the time-multiplexed complex baseband signal with asampling rate of f_(s)′=f_(s)/N.

[0073]FIGS. 8 and 9 show an example of an IQ-filter according to thepresent invention comprising a polyphase filter with branch filters oforder 2N according to the present invention. FIG. 8 shows that thepolyphase filter of order 2N as shown in FIG. 3 is used as polyphasefilter 22 according to the present invention as it is shown in FIG. 7.In FIG. 8 also quarter period sampling is used so that the carriermultiplication at the output of the polyphase filter according to thepresent invention as shown in FIG. 6 is not necessary.

[0074] In the shown example the decimation factor N is chosen to N=6.The coefficients of the IQ-filter are designed for a DAB-signal with abandwidth of 1.536 MHz. The sampling frequency is chosen to 12.288 MHzand the center frequency of the input signal is chosen to f₀=3.072 MHz.With these values equation (22) is valid.

[0075] To decrease the hardware size, the coefficients α(k) and χ(k) arequantized in a way that they can be realized by shift registers, oneadder and one subtracter. The following Table 1 shows the coefficientsof the branch allpass filters: TABLE 1 r α_(r) −χ_(r) 5 0.21875 2⁻² −2⁻⁵ 0.138671875 2⁻³ + 2⁻⁶ − 2⁻⁹ 4 0.40625 2⁻¹ − 2⁻³ + 2⁻⁵ 0.17968752⁻³ + 2⁻⁴ − 2⁻⁷ 3 0.5546875 2⁻¹ − 2⁻⁷ + 2⁻⁴ 0.171875 2⁻³ + 2⁻⁴ − 2⁻⁶ 20.6875 2⁻¹ − 2⁻⁴ + 2⁻² 0.13671875 2⁻³ + 2⁻⁶ − 2⁻⁸ 1 0.8125 1 − 2⁻² + 2⁻⁴0.08984375 2⁻⁴ + 2⁻⁵ − 2⁻⁸ 0 0.9375 1 − 2⁻⁴ 0.03125 2⁻⁵

[0076] The hardware size can further be decreased when the N timemultiplexed allpass filters and order are realized by a second timemultiplex so that the branch allpass filters of order 2N are realized bya time multiplexed allpass filter of order N. FIG. 9 shows a blockdiagram of the IQ-filter realized in a time-multiplex and multiplicationcoefficients that are realized by shift and add operation:

[0077] The “multiplier” which is realizing the first multiplier 5 aswell as the second multiplier 9 comprises a first shift register 10having a shift value of 2⁻² that is receiving the multiplicand and aninput selector switch S2 receiving the output value of said first shiftregister 10 at a first fixed input terminal and the multiplicand at asecond fixed input terminal, a second shift register 11, a third shiftregister 12 and a fourth shift register 13 each having its inputconnected to the moveable output terminal of said input selector switchS2, a third subtracter 14 receiving the output value of said secondshift register 11 at a first input receiving the minuend, a first outputselector switch 33 having its moveable input terminal connected to theoutput of said third shift register 12, its first fixed output terminalruns free and its second fixed output terminal is connected to a secondinput of the third subtracter 14 receiving the subtrahend, a third adder15 receiving the output value of said third subtracter 14 at a firstinput receiving the first summand and outputting the multipliedmultiplicand, a second output selector switch 34 having its moveableinput terminal connected to the output of said fourth register 13, itsfirst fixed output terminal runs free and its second fixed outputterminal is connected to a second input of the third adder 15 receivingthe second summand.

[0078] Furtheron, to achieve the time multiplex, the incoming signalt(k) as it is shown in FIG. 6 is fed directly to a first fixed inputterminal (which is marked with a 0 as all first fixed input terminals ofthe switches shown in the figures) of an input selector switch S0 andvia a multiplicator multiplying with −1 to a second fixed terminal ofthis input selector switch S0. The movable terminal of the inputselector switch S0 which is indicated by an arrow pointing to the firstfixed terminal of the input selector switch is connected to the secondfixed terminal of a first feedback selector switch S1. The movableoutput terminal of the first feedback selector switch S1 which isindicated by an arrow pointing to the first fixed terminal of said firstfeedback selector switch S1 is connected to the first delay element 1with a delay time 6 T, i. e. 2.3.T, that additionally comprises a latchenable input receiving the latch signal LE0 for the purpose of the timemultiplex. The output of the first delay element 1 is fed via the secondfixed terminal and the movable terminal of a second feedback selectorswitch S5 to the first input of the first adder 3. For the purpose ofthe time multiplex the first adder 3 is in this case an adder-subtracterand therewith the first input receives either the first summand or theminuent according to the respective function of the adder-subtracter 3.The output of the adder-subtracter 3 is fed to a first part 2 a of thesecond delay element that has a delay T which provides the output signalu(k) of the polyphase filter 22 according to the present invention atits output. This output signal is fed to the first fixed input terminalof the first input selector switch S1 and also to a second part 2 b ofthe second delay element having a delay 11 T. The output of this delayelement 2 b is supplied to the first fixed terminal of the secondfeedback selector switch S5 and as subtrahent to the first subtracter 4which receives the output signal of the first feedback selector switchS1 as minuent. The difference calculated by the first subtracter 4 getsmultiplied with a respective coefficient α(k) or χ(k) as described abovebefore it is supplied as second summand or as subtrahent to theadder-subtracter 3.

[0079] As mentioned above, the effient IQ-filter realization shown inFIG. 9 has its sampling rate decimation factor of N=6 and the N allpassfilters 2N^(th) order are realized time-multiplexed. Therefore, onecomplex output sample has to be processed in 12 output clock cycles, i.e. f_(c)=2 f_(s)=2.6.f_(s)′. The signal A(k) is periodic in 2 outputclock samples. Therefore, the states of the IQ-filter are periodic in 24clock cycles f_(c). Table 2 below describes for every of the 24different internal states of the IQ-filter the states of the switchesthat allabled with S0, S1, S2, S3, S4, S5, and S6 in the figures, thelatch enable signal LE0 which is active high and the shift values of theshift registers SH0, SH1, and SH2. States that are not relevant andtherefore don't care are marked by dc. Output signals w that are notdefined are marked by nd. TABLE 2 State S0 S1 S2 S3 S4 S5 S6 SH0 SH1 SH2LE0 A0 W 0 0 0 1 1 1 0 1 1 0 2 dc 1 + Q(1 − 1) 1 dc 0 0 0 0 0 0 3 dc dc0 − nd 2 0 1 1 1 1 1 1 0 0 0 2 1 + nd 3 dc 0 0 1 1 0 0 2 4 1 0 − nd 4 11 1 1 1 1 1 0 1 2 0 1 + nd 5 dc 0 0 1 1 0 0 1 4 2 0 − nd 6 1 0 1 1 1 1 11 1 5 2 1 + nd 7 dc 0 0 1 1 0 0 1 2 0 0 − nd 8 0 0 1 1 1 1 1 1 1 1 3 1 +nd 9 dc 0 0 1 1 0 0 1 3 0 0 − nd 10 0 1 1 1 1 0 1 1 2 3 dc 1 + I(1) 11dc 0 0 1 1 0 0 1 5 2 0 − nd 12 1 1 1 1 1 0 1 1 0 2 dc 1 + Q(1) 13 dc 0 00 0 0 0 3 dc dc 0 − nd 14 1 0 1 1 1 1 1 0 0 0 2 1 + nd 15 dc 0 0 1 1 0 02 4 1 0 − nd 16 0 0 1 1 1 1 1 0 1 2 0 1 + nd 17 dc 0 0 1 1 0 0 1 4 2 0 −nd 18 0 1 1 1 1 1 1 1 1 5 2 1 + nd 19 dc 0 0 1 1 0 0 1 2 0 0 − nd 20 1 11 1 1 1 1 1 1 1 3 1 + nd 21 dc 0 0 1 1 0 0 1 3 0 0 − nd 22 1 0 1 1 1 0 11 2 3 dc 1 + I(1 + 1) 23 dc 0 0 1 1 0 0 1 5 2 0 − nd

[0080] Depending on the sideband that is required for the IQ-generation,the switch S0 is switched according to the left or right states that aredescribed in the column of S0 in Table 2.

[0081] Preferably the filter can be used in a combinedDAB/FM/AM-receiver and in case of DAB-reception, the input signal with acenter frequency of f₀=3.072 MHz is sampled with a sampling rate off_(s)=12.288 MHz, in case of FM-reception, the input signal with acenter frequency of f₀=10.75 MHz is sampled with a sampling rate off_(s)=6.144 MHz and in the case of AM-reception, the input signal with acenter frequency of f₀=455 KHz is sampled with a sampling rate off_(s)=2.048 MHz.

[0082] A digital IQ-filter according to the present invention has alinear phase response in the passband and high suppression of mirroredfrequencies, since frequency modulated signals are sensitive againstgroup delay distorsions which are caused by filters with non-linearphase in the passband.

[0083] As can be seen, the realization of the IQ filter according to thepresent invention is highly efficient, since only five adders and nomultipliers are required. Therefore, the digital generation of a complexbaseband signal in combination with noise shaping and neighbour channelsuppression with a polyphase filter according to the present inventionhas low realization costs.

1. Polyphase filter consisting of N branch allpass filters of order x.Nto filter an input signal t(k), characterized by a structure of anallpass filter of order x comprising delay elements with a delay 1 andat least one multiplier, wherein all delay elements with a delay 1 arereplaced by delay elements with a delay N, and a sampling ratef_(s)′=f_(s)/N, with f_(s) being the sampling rate of the input signal(t(k)).
 2. Filter according to claim 1, characterized in that said atleast one multiplier respectively comprises N time-multiplexedmultiplication coefficients (α₀, . . . , α_(N−1); χ₀, . . . , χ_(N−1))that are used in a predetermined order (α(k)=α_((k mod N));χ(k)=χ_((k mod N))).
 3. Filter according to claim 1 or 2, characterizedby: a first delay element (1) with a delay N that receives the inputsignal (t(k)); a first adder (3) that receives the output signal of saidfirst delay element (1) at a first input for the first summand; a seconddelay element (2) with a delay N that receives the sum produced by saidfirst adder (3); a first subtracter (4) that receives the input signal(t(k)) at a first input for the minuend and the output signal of thesecond delay element (2) at a second input for the subtrahend; and afirst multiplier (5) that receives the calculated difference of thefirst subtracter (4), multiplies it respectively with a predeterminedmultiplication coefficient (α(k)) and outputs the calculated product toa second input of the first adder (3) that receives the second summand,wherein in case x equals to 1 the sum produced by said first adder (3)builds the output signal (u(k)) of the branch allpass filters.
 4. Filteraccording to claim 3, characterized by: a second adder (6) that receivesthe output signal of the second delay element (2) at a first input forthe first summand; a third delay element (7) with a delay N thatreceives the sum produced by said second adder (6); a second subtracter(8) that receives the sum produced by said first adder (3) at a firstinput for the minuend and the output signal of the third delay element(7) at a second input for the subtrahend; and a second multiplier (9)that receives the calculated difference of the second subtracter (8),multiplies it respectively with a predetermined multiplicationcoefficient (_(χ)(k)) and outputs the calculated product to a secondinput of the second adder (6) that receives the second summand, whereinin case x equals to 2 the sum produced by said second adder (6) buildsthe output signal (u(k)) of the branch allpass filters.
 5. Filteraccording to anyone of claims 2 to 4, characterized in that every one ofsaid at least one multipliers (5, 9) has quantised coefficients so thatit can be realised by at least one shift register, at least one adder orat least one subtracter.
 6. Filter according to claim 5, characterizedin that one multiplier (5, 9) comprises: a first shift register (10)having a shift value of 2⁻² that is receiving the multiplicand and, aninput selector switch (S2) receiving the output value of said firstshift register (10) at a first fixed input terminal and the multiplicandat a second fixed input terminal, a second shift register (11), a thirdshift register (12) and a fourth shift register (13) each having itsinput connected to the moveable output terminal of said input selectorswitch (S2), a third subtracter (14) receiving the output value of saidsecond shift register (11) at a first input receiving the minuend, afirst output selector switch (S3) having its moveable input terminalconnected to the output of said third shift register (12), its firstfixed output terminal runs free and its second fixed output terminal isconnected to a second input of the third subtracter (14) receiving thesubtrahend, a third adder (15) receiving the output value of said thirdsubtracter (14) at a first input receiving the first summand andoutputting the multiplied multiplicand, a second output selector switch(S4) having its moveable input terminal connected to the output of saidfourth shift register (13), its first fixed output terminal runs freeand its second fixed output terminal is connected to a second input ofthe third adder (15) receiving the second summand.
 7. Filter accordingto anyone of the preceding claims, characterized in that a polyphasefilter of order x.N with x=a is realised in a time multiplex and workswith a clock frequency f_(c)=a·f_(s).
 8. IQ-generator, characterized inthat an incoming sampled bandpass signal s(k) gets multiplied by asignal A(k)=(−1)^(floor (k/N)) before being supplied as input signalt(k) to a polyphase filter consisting of N branch allpass filters (22)of order x.N.
 9. IQ-generator according to claim 8, characterized inthat the output signal of the polyphase branch allpass filters (22) getsmultiplied by a signal B(k)·cos(2πf₀/f_(s)·k) to calculate theI-component of the complex baseband signal and by a signalB(k)·sin(2πf₀/f_(s)·k) to calculate the Q-component of the complexbaseband signal with A(k)=B(k)=(−1)^(floor(k/n)).
 10. IQ-generatoraccording to claim 8 or 9, characterized by one polyphase filteraccording to anyone of claims 1 to 7 to filter the I-component and theQ-component of a complex baseband signal.